The club could not be immediately reached for a comment.
Bayern came calling again in 2011, and enjoyed a trophy-laden two seasons under Heynckes.
After winning the German title in 2016/17, Ancelotti was sacked last week in the wake of Bayern's 3-0 Champions League defeat to Paris Saint-Germain.
Bayern have confirmed that Heynckes will officially become the club's manager on Monday on a contract until the end of the season, with Peter Hermann and Hermann Gerland to be his assistants.
Heynckes, who retired four years ago, turned the Bavarians into one of Europe's most dominant teams, culminating in the treble-winning side of 2013, and has been drafted in on a short-term deal.
But, Bayern too close to the heart. His appointment had been delayed while Bayern waited for Hermann to be released by second-division club Fortuna Duesseldorf, where he was a coach. We are very grateful to Jupp.
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Heynckes added: "I wouldn't have returned to any other club in the world, but Bayern Munich is a love affair for me. He's the ideal coach for FC Bayern at this moment in time".
Ancelotti who was in Jerusalem to host a special training session for local kids as part of the assist for peace project, said he wants to manage, not this season, but next season, probably in the premier league or another top flight league. My coach team and I will now present everything that the team will present the fans soon again successful football. "I'm really looking forward to this task".
Work in Spain followed, at Athletic Bilbao, Tenerife and Real Madrid, where he won the Champions League in 1997.
Hermann worked with Heynckes for two seasons at Bayer Leverkusen and then another two at Bayern before both signed off with the treble in 2013.
This would be the 72-year-old's fourth spell with the German giants.
Heynckes first took the reins at Bayern in 1987.